Quantum Mechanical Theory Research Articles

Challenges in sensemaking and reasoning in the context of degenerate perturbation theory in quantum mechanics

We discuss an investigation of student sensemaking and reasoning in the context of degenerate perturbation theory (DPT) in quantum mechanics. We find that advanced undergraduate and graduate students in quantum physics courses often struggled with expertlike sensemaking and reasoning to solve DPT problems. The sensemaking and reasoning were particularly challenging for students as they tried to integrate physical and mathematical concepts to solve DPT problems. Their sensemaking showed local coherence but lacked global consistency with different knowledge resources getting activated in different problem-solving tasks even if the same concepts were applicable. Depending upon the issues involved in the DPT problems, students were sometimes stuck in the “physics mode” or “math mode” and found it challenging to coordinate and integrate the physics and mathematics appropriately to solve quantum mechanics problems involving DPT. Their sensemaking shows the use of various reasoning primitives. It also shows that some advanced students struggled with self-monitoring and checking their answers to make sure they were consistent across different problems. Some also relied on memorized information, invoked authority, and did not make appropriate connections between their DPT problem solutions and the outcomes of experiments. Advanced students in quantum mechanics often displayed analogous patterns of challenges in sensemaking and reasoning as those that have been found in introductory physics. Student sensemaking and reasoning show that these advanced students are still developing expertise in this novel quantum physics domain as they learn to integrate physical and mathematical concepts. Published by the American Physical Society 2024

Sayed`s Theory in Quantum Mechanics: An Innovative Approach for Wave Function Equations Measurability, Efficacy and Universality

Allah (God) is ubiquitous and the only Creator of Everything. Quantum mechanics is the world of the microscopic scale of physics. The universe is a macroscopic manifestation of the quantum approach. In this revolutionary article, correctness and rectification of Schrodinger wave equations that has huge limitations and shortcomings, were proudly achieved. The Sayed quantum wave function (SQWF) was derived and defined (Ψs) for free electron and in Laplace coordinates as a function in wavelength and light speed. The SQWF was calculated and quantified for de Broglie moving electron; 0.4033x10-20 Second. Using SQWF equation, the speed of light was accurately calculated; ~3x108 m/s. respectively. An outstanding Sayed`s quantum wavelength (SQW) was proposed and elucidated. The Sayed time dependent wave function equations (STDWFE) were derived and given to be a generic alternative to deal with all atoms rather than the one electron atoms of Schrodinger. The crucial parameters; wavelength, Rydberg constant RH, atomic number, principle quantum number, and mc2 were introduced in the STDWFE. It is a quantized formula. The (Ψs) was calculated for H, He, B and found to be , ,The Sayed quantum constantRH mc2, was quantified to be 8.93x10-7 J/m.

Second-order dissociation and transition of heavy quarkonia in the quark-gluon plasma

We revisit the dissociation of heavy quarkonia by thermal partons at the next-to-leading order (NLO, also known as inelastic parton scattering dissociation) in the quark-gluon plasma (QGP). Utilizing the chromoelectric dipole coupling from quantum chromodynamics (QCD) multipole expansion as an effective Hamiltonian, this has been conducted in the approach of second-order quantum mechanical perturbation theory, which allows us to systematically incorporate the bound state wave functions. Employing the quarkonium wave functions and binding energies obtained from an in-medium potential model, we then numerically evaluate the dissociation cross sections and rates for various charmonia and bottomonia, where the infrared and collinear divergences are regularized by the thermal masses of medium partons. We demonstrate that distinct from the leading order (LO, also known as gluo-dissociation) counterparts peaking at relatively low gluon energy and falling off thereafter, the NLO cross sections first grow and then nearly saturate as the incident parton energy increases, as a result of the outgoing parton carrying away the excess energy. The resulting NLO dissociation rates increase with temperature and take over from the LO counterparts toward high temperatures, similar to pertinent findings from previous studies. We also evaluate the in-medium second-order transition between different bound states, which may contribute to the total thermal decay widths of heavy quarkonia in the QGP. Published by the American Physical Society 2024

Superluminal matter waves

The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the velocity is less than the vacuum speed of light. Here, we show that the Dirac equation admits free-particle solutions where the peak amplitude of the wave function can travel at any velocity, including those exceeding the vacuum speed of light, despite having a subluminal velocity expectation value. The solutions are constructed by superposing basis functions with correlations in momentum space. These arbitrary velocity wave functions feature a near-constant profile and may impact quantum mechanical processes that are sensitive to the local value of the probability density as opposed to expectation values. Published by the American Physical Society 2024

Stable-to-unstable transition in quantum friction

We investigate the frictional force arising from quantum fluctuations when two dissipative metallic plates are set in a shear motion. While early studies showed that the electromagnetic fields in the quantum friction setup reach nonequilibrium steady states, yielding a time-independent force, other works have demonstrated the failure to attain steady states, leading to instability and time-varying friction under sufficiently low-loss conditions. Here, we develop a fully quantum-mechanical theory without perturbative approximations, and we unveil the transition from stable to unstable regimes of the quantum friction setup. Due to the relative motion of the plates, their electromagnetic response may be active in some conditions, resulting in optical gain. We prove that the standard fluctuation-dissipation leads to inconsistent results when applied to our system, and, in particular, it predicts a vanishing frictional force. Using a modified fluctuation-dissipation relation tailored for gain media, we calculate the frictional force in terms of the system Green's function, thereby recovering early works on quantum friction. Remarkably, we also find that the frictional force diverges to infinity as the relative velocity of the plates approaches a threshold. This threshold is determined by the damping strength and the distance between the metal surfaces. Beyond this critical velocity, the system exhibits instability, akin to the behavior of a laser cavity, where no steady state exists. In such a scenario, the frictional force escalates exponentially. Our findings pave the way for experimental exploration of the frictional force in proximity to this critical regime. Published by the American Physical Society 2024

Effective modeling of open quantum systems by low-rank discretization of structured environments.

The accurate description of the interaction of a quantum system with its environment is a challenging problem ubiquitous across all areas of physics and lies at the foundation of quantum mechanics theory. Here, we pioneer a new strategy to create discrete low-rank models of the system-environment interaction, by exploiting the frequency and time domain information encoded in the fluctuation-dissipation relation connecting the system-bath correlation function and the spectral density. We demonstrate the effectiveness of our methodology by combining it with tensor-network methodologies and simulating the quantum dynamics of complex excitonic systems in a highly structured bosonic environment. The new modeling framework sets the basis for a leap in the analysis of open quantum systems, providing controlled accuracy at significantly reduced computational costs, with benefits in all connected research areas.

Investigation of Phosphazene Superbase Interactions with [PCl2N]3.

In this study, the reaction between phosphazene superbases and a chlorophosphazene trimer ([PCl2N]3) has been investigated. In this room temperature reaction, the phosphazene superbase (Me2N)3PN(Me2N)2P═NEt, commonly known as P2Et, was shown to behave as a nucleophile, displacing one of the chlorides from [PCl2N]3 and producing the tadpole-like structure 1. The reaction described herein is one of the few instances of a phosphazene superbase behaving as a nucleophile rather than a Brønsted base. Once formed, this structure contains contrasting reactivity, containing a weakly basic phosphazene head while maintaining a highly basic phosphazene tail of the tadpole. The mechanism of the reaction was explored by investigating the potential energy surface through density functional theory calculations at the B3LYP/6-311+G(d,p) level of quantum mechanical theory. It was determined that the reaction of P2Et with [PCl2N]3 followed a stepwise process beginning with the substitution of P2Et onto [PCl2N]3 with the concurrent loss of chloride. Subsequently, the chloride attacks the ethyl group of the P2Et moiety, and ethyl chloride is released, producing 1. Compound 1 was further characterized via 31P NMR spectroscopy, mass spectrometry, and X-ray crystallography.

Fundamental Laws and Quantum Dynamics

Background: Recently, we obtained a unitary theory of quantum mechanics and general relativity, where a quantum particle is a continuous distribution of matter in the two conjugate spaces of the coordinates and momentum, quantized by the equality of the mass parameter describing the relativistic dynamics of the matter, with the mass as an integral of the matter density. However, in this framework, we have not explicitly revealed the connection between our new theory and the fundamental laws of quantum mechanics. Methods: We analyzed in detail the three fundamental laws of quantum mechanics, explicitly describing experimental data: 1) Planck’s law of the blackbody electromagnetic radiation of a system of electrically charged harmonic oscillators, 2) Einstein’s law of the photon energy proportionality with the photon frequency, and 3) de Broglie’s law of the quantum particle as an oscillator in space. Results: We reobtained the two dynamical equations, in the conjugate spaces of the coordinates and momentum, as functions of the Lagrangian system, unlike the Schrödinger equation, depending on the Hamiltonian. Conclusion: According to the fundamental laws of quantum mechanics, a quantum particle is a continuous distribution of matter with an intrinsic mass, unlike the conventional quantum mechanics for the state occupation probabilities of punctual entities moving with the light velocity and getting an apparent mass only by collisions with some bosons pervading the whole universe. According to these laws, we obtained a quantum theory in agreement with common sense, classical logic, and general relativity.

Quantum mechanics emerging from complex Brownian motions

The connection between the Schrödinger equation and Einstein's diffusion theory based on the Brownian motion of independent particles is well known. However, in contrast to diffusion theory, quantum mechanics theory has suffered controversial interpretations due to the counterintuitive concept of wavefunction. Here, while we confirm there is no difference in the mathematical form of these two equations, we derive the imaginary version of displacement. Using the diffusion theory of particles in a medium, as simple as it is, we describe that quantum mechanics is just an elegant and subtle equation to describe the probability of all the trajectories that a particle can take to propagate in time by a predictive wavefunction. Therefore, information on the position of particles through time in quantum theory is embedded in the wavefunction, which predicts the evolution of an ensemble of individual Brownian particles.

Quantum geometric perspective on the origin of quantum-conditioned curvatures

Abstract The quantization of the gravitational field, which includes the metric field, has been investigated using various methods such as loop quantum gravity, quantum field theory, and string theory. Nevertheless, an alternative strategy to tackle the challenge of merging the fundamentally different theories of general relativity (GR) and quantum mechanics (QM) is through a quantum geometric approach. This particular approach entails extending QM to relativistic energies and finite gravitational fields, while also expanding the continuous Riemann to a discretized (quantized) Finsler-Hamilton geometry. By embracing this method, it may be feasible to bridge the gap between GR and QM or even achieve their unification. The resulting fundamental tensor appears to blend its original classical and quantum characteristics, effectively integrating quantum-mechanically induced revisions to the affine connections and spacetime curvatures. Our study primarily focuses on investigating the Ricci curvature tensor in the context of the Einstein-Gilbert-Straus metric. By employing both analytical and numerical methods, we have identified quantum-conditioned curvatures (QCC) that act as additional sources of gravitation. These QCC exhibit a fundamental difference from the traditional curvatures described by Einsteinian GR. While the Ricci curvatures are predominantly positive across most regions, the quantized Ricci curvatures display negativity. We conclude that the QCC a) possess an intrinsic, essential, and real character, b) should not be disregarded due to their significant magnitude, and c) are fundamentally different from the curvatures found in classical GR. Moreover, we conclude that the proposed quantum geometric approach may offer an alternative mathematical framework for understanding the emergence of quantum gravity.

Intrinsic squeezing of mechanical motion of a harmonically trapped atom with spin-orbit coupling

In this paper we investigated one-dimensional harmonically trapped atom with Raman-induced spin-orbit coupling by mapping to quantum-like model. Using displacement Fock states in quantum optics and variational methods we found the odd-parity superposition state of left- and right-displaced oscillator state is a good approximate solution to the ground state, which captures the essential physics of the system. The ground state wave function owes nodes which is remarkably different from the conventional no-node theory in quantum mechanics. The results show the atomic motion of center of mass exhibits intrinsic squeezing properties with relation to the Raman and spin-orbit coupling strength characterized by the variance in position and momentum, information entropy, as well as the Wigner function of the ground state. The dynamics of center of mass are also studied which demonstrates intuitive Zitterbewegung oscillations in momentum space and real space. Our results could be used for observing Zitterbewegung oscillations in neutral atomic gases and engineering nonclassic states.

Relativistic generalized uncertainty principle for a test particle in four-dimensional spacetime

The generalized uncertainty principle provides a promising phenomenological approach to reconciling the fundamentals of general relativity with quantum mechanics. As a result, noncommutativity, measurement uncertainty, and the fundamental theory of quantum mechanics are subject to finite gravitational fields. The generalized uncertainty principle (RGUP) on curved spacetime allows for the imposition of quantum-induced elements on general relativity (GR) in four dimensions. In the relativistic regimes, the determination of a test particle’s spacetime coordinates, [Formula: see text], becomes uncertain. There exists a specific range of coordinates where the accessibility to [Formula: see text] is notably limited. Consequently, the spacetime coordinates lack both smoothness and continuity. The quantum-mechanical calculations of the spacetime coordinates are directly linked to their measurement through the expectation value [Formula: see text]. This expectation value is dependent on [Formula: see text], which is itself limited by a minimum measurable length [Formula: see text]. A crucial finding presented in this script is the existence of a lower bound for the Hamiltonian, which implies the stability of the quantum nature of spacetime. The direct correlation between [Formula: see text] and [Formula: see text] is a significant discovery, suggesting a proportional relationship. The conjecture is made that the primary metric g carries all essential information regarding spacetime curvature and serves a role akin to the Jacobian determinant in general relativity. Moreover, the linear relationship between [Formula: see text] and the Planck length [Formula: see text] is established with a proportionality factor of [Formula: see text], where [Formula: see text] denotes the RGUP parameter. The discretization of spacetime coordinates results in the discontinuity of the test particle’s wavefunction [Formula: see text], leading to an unrealistic [Formula: see text]. It is also noted that the lower limit of [Formula: see text] is directly proportional to the fundamental tensor.

Theoretical justification for obtaining new nanomaterials by taking into account the influence of three main factors

By generalizing and transferring the results of the Marcus theory for homogeneous reactions to heterogeneous, Dogonadze and Kuznetsov created a quantum-mechanical theory of electrode reactions for ionic melts, the methodological principles of which allow more adequately evaluating the results of certain experimental methods of obtaining new substances with given properties. Such methods include high-temperature electrochemical synthesis (HES), the implementation of which is complicated by the lack of precise understanding of the mechanism of multi-electron processes of reduction of various ionic forms of refractory metals and nonmetals in ionic melts, including those containing molybdate and tungstate ions, both constantly and simultaneously.

QuanTest: Entanglement-Guided Testing of Quantum Neural Network Systems

Quantum Neural Network (QNN) combines the Deep Learning (DL) principle with the fundamental theory of quantum mechanics to achieve machine learning tasks with quantum acceleration. Recently, QNN systems have been found to manifest robustness issues similar to classical DL systems. There is an urgent need for ways to test their correctness and security. However, QNN systems differ significantly from traditional quantum software and classical DL systems, posing critical challenges for QNN testing. These challenges include the inapplicability of traditional quantum software testing methods to QNN systems due to differences in programming paradigms and decision logic representations, the dependence of quantum test sample generation on perturbation operators, and the absence of effective information in quantum neurons. In this paper, we propose QuanTest, a quantum entanglement-guided adversarial testing framework to uncover potential erroneous behaviors in QNN systems. We design a quantum entanglement adequacy criterion to quantify the entanglement acquired by the input quantum states from the QNN system, along with two similarity metrics to measure the proximity of generated quantum adversarial examples to the original inputs. Subsequently, QuanTest formulates the problem of generating test inputs that maximize the quantum entanglement adequacy and capture incorrect behaviors of the QNN system as a joint optimization problem and solves it in a gradient-based manner to generate quantum adversarial examples. Experimental results demonstrate that QuanTest possesses the capability to capture erroneous behaviors in QNN systems (generating 67.48%-96.05% more high-quality test samples than the random noise under the same perturbation size constraints). The entanglement-guided approach proves effective in adversarial testing, generating more adversarial examples (maximum increase reached 21.32%).

Benchmarking Quantum Mechanical Levels of Theory for Valence Parametrization in Force Fields.

A wide range of density functional methods and basis sets are available to derive the electronic structure and properties of molecules. Quantum mechanical calculations are too computationally intensive for routine simulation of molecules in the condensed phase, prompting the development of computationally efficient force fields based on quantum mechanical data. Parametrizing general force fields, which cover a vast chemical space, necessitates the generation of sizable quantum mechanical data sets with optimized geometries and torsion scans. To achieve this efficiently, choosing a quantum mechanical method that balances computational cost and accuracy is crucial. In this study, we seek to assess the accuracy of quantum mechanical theory for specific properties such as conformer energies and torsion energetics. To comprehensively evaluate various methods, we focus on a representative set of 59 diverse small molecules, comparing approximately 25 combinations of functional and basis sets against the reference level coupled cluster calculations at the complete basis set limit.

The cosmological switchback effect. Part II

Recent developments in static patch holography proposed that quantum gravity in de Sitter space admits a dual description in terms of a quantum mechanical theory living on a timelike surface near the cosmological horizon. In parallel, geometric observables associated with the Einstein-Rosen bridge of a black hole background were suggested to compute the computational complexity of the state dual to a gravitational theory. In this work, we pursue the study of the complexity=volume and complexity=action conjectures in a Schwarzschild-de Sitter geometry perturbed by the insertion of a shockwave at finite boundary times. This analysis extends previous studies that focused either on the complexity=volume 2.0 conjecture, or on the case of a shockwave inserted along the cosmological horizon. We show that the switchback effect, describing the delay in the evolution of complexity in reaction to a perturbation, is a universal feature of the complexity proposals in asymptotically de Sitter space. The geometric origin of this phenomenon is related to the causal connection between the static patches of de Sitter space when a positive pulse of null energy is inserted in the geometry.

Tunnel transport problem for open multilayer nitride nanostructures with an applied constant magnetic field and time-dependent potential: An exact solution

A quantum mechanical theory for description of electronic quasistationary states in two-dimensional (2D) layered semiconductor nanostructure was developed. A constant external magnetic field B was directed along semiconductor layers. The presence of internal electric fields F originated from the potential barriers and wells in semiconductor layers was taken into account. The vector of F was directed perpendicularly to semiconductor layers. The interaction of tunneled electrons with a time-dependent electromagnetic fields was analyzed in detail. An approach to obtain an exact solution to the problem based on a combination of the Lewis-Riesenfeld method for complete Schrödinger equation and scattering theory was developed. Application of the scattering theory in combination with the -matrix and transfer-matrix methods allowed us to calculate the electron quasistationary spectra. Effects of magnetic field on the resonant energy and width of electronic quasistationary states as well as on the electronic conductivity were also discussed. Published by the American Physical Society 2024

Learning together: Towards foundation models for machine learning interatomic potentials with meta-learning

The development of machine learning models has led to an abundance of datasets containing quantum mechanical (QM) calculations for molecular and material systems. However, traditional training methods for machine learning models are unable to leverage the plethora of data available as they require that each dataset be generated using the same QM method. Taking machine learning interatomic potentials (MLIPs) as an example, we show that meta-learning techniques, a recent advancement from the machine learning community, can be used to fit multiple levels of QM theory in the same training process. Meta-learning changes the training procedure to learn a representation that can be easily re-trained to new tasks with small amounts of data. We then demonstrate that meta-learning enables simultaneously training to multiple large organic molecule datasets. As a proof of concept, we examine the performance of a MLIP refit to a small drug-like molecule and show that pre-training potentials to multiple levels of theory with meta-learning improves performance. This difference in performance can be seen both in the reduced error and in the improved smoothness of the potential energy surface produced. We therefore show that meta-learning can utilize existing datasets with inconsistent QM levels of theory to produce models that are better at specializing to new datasets. This opens new routes for creating pre-trained, foundation models for interatomic potentials.

A link between static and dynamical perturbation theory

Dynamics, the physical change in time and a pillar of natural sciences, can be regarded as an emergent phenomenon when the system of interest is part of a larger, static one. This ‘relational approach to time’, in which the system’s environment provides a temporal reference, does not only provide insight into foundational issues of physics, but holds the potential for a deeper theoretical understanding as it intimately links statics and dynamics. Reinforcing the significance of this connection, we demonstrate, based on recent progress (Gemsheim and Rost 2023 Phys. Rev. Lett. 131 140202), the role of emergent time as a vital link between time-independent and time-dependent perturbation theory in quantum mechanics. We calculate first order contributions, which are often the most significant, and discuss the issue of degenerate spectra. Based on our results, we envision future applications for the calculation of dynamical phenomena based on a single pure energy eigenstate.

Even and Odd Cat States of Two and Three Qubits in the Probability Representation of Quantum Mechanics.

We derive the probability representation of even and odd cat states of two and three qubits. These states are even and odd superpositions of spin-1/2 eigenstates corresponding to two opposite directions along the z axis. The probability representation of even and odd cat states of an oscillating spin-1/2 particle is also discussed. The exact formulas for entangled probability distributions describing density matrices of all these states are obtained.